Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this development, we study a deep neural network method to estimate the drift coefficient of a multi-dimensional diffusion process from discrete observations. We derive generalization error bounds for least squares estimates based on deep neural networks and show that they achieve the minimax rate of convergence up to a logarithmic factor when the drift function has a compositional structure.

翻译：最近,许多研究揭示了非对称回归模型中深神经网络方法高度适应性,并且为各种功能类别确定了其优异性能。受这一发展驱动,我们研究了一种深神经网络方法,从离散观测中估算多维扩散过程的漂移系数。我们从深神经网络中得出了最小方位估计的概括性误差,并表明在漂移函数具有组成结构时,它们达到了最小的趋同率,达到对数系数。